Advertisement

An Approach Theoretic Version of Anscombe’s Theorem with an Application in Biostatistics

  • Ben Berckmoes
Article
  • 14 Downloads

Abstract

We establish an approach theoretic version of Anscombe’s theorem, which we apply to justify the use of confidence intervals based on the sample mean after a group sequential trial.

Keywords

Anscombe’s theorem Approach theory Asymptotic normality Confidence intervals Group sequential trial Sample mean 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Anscombe, F.J.: Large-sample theory of sequential estimation. Proc. Camb. Philos. Soc. 48, 600–607 (1952)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bartroff, J., Lai, T.L., Shih, M.-C.: Sequential Experimentation in Clinical Trials. Design and Analysis. Springer Series in Statistics. Springer, New York (2013)CrossRefMATHGoogle Scholar
  3. 3.
    Berckmoes, B., Ivanova, A., Molenberghs, G.: On the sample mean after a group sequential trial. https://arxiv.org/abs/1706.01291 (2017)
  4. 4.
    Emerson, S.S., Fleming, T.R.: Parameter estimation following group sequential hypothesis testing. Biometrika 77, 875–892 (1990)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gut, A.: Stopped Random Walks. Limit Theorems and Applications. Applied Probability. A Series of the Applied Probability Trust, vol. 5. Springer, New York (1988)CrossRefMATHGoogle Scholar
  6. 6.
    Gut, A.: Anscombe’s theorem 60 years later. Sequ. Anal. 31(3), 368–396 (2012)MathSciNetMATHGoogle Scholar
  7. 7.
    Hughes, M.D., Pocock, S.J.: Stopping rules and estimation problems in clinical trials. Stat. Med. 7, 1231–1242 (1988)CrossRefGoogle Scholar
  8. 8.
    Lowen, R.: Index Analysis. Approach Theory at Work. Springer Monographs in Mathematics. Springer, London (2015)MATHGoogle Scholar
  9. 9.
    Molenberghs, G., Kenward, M.G., Aerts, M., Verbeke, G., Tsiatis, A.A., Davidian, M., Rizopoulos, D.: On random sample size, ignorability, ancillarity, completeness, separability, and degeneracy: sequential trials, random sample sizes, and missing data. Stat. Methods Med. Res. 23(1), 11–41 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Woodroofe, M.: Estimation after sequential testing: a simple approach for a truncated sequential probability ratio test. Biometrika 79(2), 347–353 (1992)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universiteit AntwerpenAntwerpBelgium

Personalised recommendations